Using Karen Fonstad's map and mileage, The Lonely Mountain is about 250 miles away. The question is, could The Company have seen the peak at that distance? There is a formula:

The formula for calculating maximum line of sight distance d is

d = SQRT (2Rh + h EXP 2) where R is radius of Earth and h is height above sea level an approximation when h << R is d = SQRT (13h) using metric values For a 14,000 foot peak that would give about 145-200 miles maximum line of sight distance.

So, if the Carrock is tall enough...higher than 14,000...it may be possible to just see the peak, with the help of oxygen tanks.

the Lonely Mountain to be in these films? In looking up the height online for the Lonely Mountain it is said to be around 3,500 ft ( Minas Tirith was 1,000 ft plus up to the white tower of Ecthelion). Probably could not be seen from that far at that height. But at 12,000-14,000 feet it could probably be seen from there above Mirkwood.

I can see Mt. Rainier (14,409 foot elevation) from my home, but it is only 80 miles away, and I am about 210 feet above sea level.

The stretch is Bilbo and the others seeing it at all over Mirkwood from that distance, even from the Carrock. In the book, Bilbo's first sight of the Lonely Mountain is after he escaped with the Dwarves on the barrels, and is approaching Long Lake. " Well well!", said a voice. "Just look! Bilbo the hobbit on a pony, my dear! Isn't it delicious!" "Most astonishing wonderful!"

It just has to be 14,000 above sea level is how I'm reading the formula. I'm sitting over a mile high (5,280 feet) as I type this and I'm about 6 miles away from the closest mountain.

Does it affects things if the mountian being viewed is at a lower elevation? From memory, driving over some of the highest passes in north-central Colorado, I can make out mountain ranges that are in the southern part of the state and they would be at least 200 to 250 miles away.

I'm not saying the movie didn't exaggerate, because I think it did (just like looking at the mountains of Mordor from Gondor in ROTK) but, from my own experience living in a state with lots of mountains, I don't think it exaggerated completely beyond belief.

"At last they came up the long road, and reached the very pass where the goblins had captured them before. But they came to that high point at morning, and looking backward they saw a white sun shining over the out-stretched lands. There behind lay Mirkwood, blue in the distance, and darkly green at the nearer edge even in the spring. There far away was the Lonely Mountain on the edge of eyesight. On its highest peak snow yet unmelted was gleaming pale. "So comes snow after fire, and even dragons have their ending!" said Bilbo, and he turned his back on his adventure."

It's a picture of the view from the top of Mount Evans here in Colorado. One of the things noted in the sign are the Sangre de Cristo mountains which are almost 200 miles away. Of course, you can't see them very well, which is why I said they definitely did exaggerate in the movie. Besides, the Carrock would probably have to be above the tree-line for them to see so far and it didn't look like it was in the movie.

I do think it's important that this view by Bilbo is on the journey home, when Bilbo departs from Wilderland. Tolkien saves the first view of the Lonely Mountain for after the Barrel Escape to add drama and impact when the company first arrive at the ominous location of their quest.

"At last they came up the long road, and reached the very pass where the goblins had captured them before. But they came to that high point at morning, and looking backward they saw a white sun shining over the out-stretched lands. There behind lay Mirkwood, blue in the distance, and darkly green at the nearer edge even in the spring. There far away was the Lonely Mountain on the edge of eyesight. On its highest peak snow yet unmelted was gleaming pale. "So comes snow after fire, and even dragons have their ending!" said Bilbo, and he turned his back on his adventure."

And yes, Tolkien did that stretching or shrinking of geography all the time as well. In LotR there are several occasions that do not make sense.

I "found" a thorough (but not exhaustive) recent discussion of this question.
[In reply to]

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Here, on the Mythopoeic Society mail list. See also the responses, particularly those by Troels Forchhammer.

Short version: The distances at which Tolkien describes the most-distant mountains being visible are at the extreme edge of possibility, and that only if the atmospheric phenomenon called "looming" is present (as Plurmo has noted). Tolkien's presentation of such images is believable: they are barely visible smudges on the horizon. Jackson, if the distances in his films are the same as in the books, does not. His Lonely Mountain looks like a peak less than half as far from the Carrock as Tolkien would have it. (Even granted that it's taller than Tolkien's mountain.) So it appears that in The Hobbit movie, as in The Lord of the Rings movies before, the world is smaller than it is in Tolkien. -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- <><><><><><><><><><><><><><><><><><><><> Discuss Tolkien's life and works in the Reading Room! +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+= How to find old Reading Room discussions.